Doppler processing apparatus and method

ABSTRACT

In a doppler processor system including an inertial guidance platform and a coherent radar having an azimuthally scanning antenna, the scan rate of which is substantially constant over all portions of the scan region, computing means for computing the on-boresight doppler velocity Vfd and the time rate of change of the doppler velocity V fd whereby the use of function potentiometers mounted on the radar antenna gimbal system is avoided, and increased utilization is made of an onboard computer. Direction matrix conversion computing means, responsive to said radar and to said inertial platform, provides a first and second output corresponding to a respective one of a preselected derivative of the doppler velocity and the product sEANVzRAD, where: SEAN sine of the antenna elevation angle VzRAD platform velocity resolved in the coordinates of the radar system. A first analog integrator responsive to said first output of the computing means provides a signal indicative of V fd; and signal combining means having a first and second input, responsive to a respective one of said second output of the computing means and to the double integral with respect to time of the first output of the computing means, provides a signal indicative of Vfd.

ited States Patent [72] Inventor Jacob E. Valstar Orange, Calif. [211 App]. No. 779,943 [22] Filed Nov. 29, 1968 [45] Patented Dec. 7, 1971 [73] Assignee North American Rockwell Corporation [54] DOPPLER PROCESSING APPARATUS AND METHOD 7 Claims, 4 Drawing Figs.

[52] U.S. Cl. 343/8, 343/9 [51] Int. Cl G0ls 9/46 [50] Field 01 Search 343/8, 9,5 DP; 244/319, 3.20

[56] References Cited UNITED STATES PATENTS 3,131,390 4/1964 Condie et al 343/8 3,140,482 7/1964 Duncan et al.... 343/8 X 3,214,575 10/1965 Seliger et al. 343/8 3,414,899 12/1968 Buell 343/9 Pitts lNERTlAL PLATFORM ABSTRACT: in a doppler processor system including an inertial guidance platform and a coherent radar having an azimuthally scanning antenna, the scan rate of which is substantially constant over all portions of the scan region, computing means for computing the on-boresight doppler velocity V and the time rate of change of the doppler velocity V whereby the use of function potentiometers mounted on the radar antenna gimbal system is avoided, and increased utilization is made of an onboard computer. Direction matrix conversion computing means, responsive to said radar and to said inertial platform, provides a first and second output corresponding to a respective one of a preselected derivative of the doppler velocity and the product sE -V where:

sE sine of the antenna elevation angle V platform velocity resolved in the coordinates of the radar system.

A first analog integrator responsive to said first output of the computing means provides a signal indicative of V m; and signal combining means having a first and second input, responsive to a respective one of said second output of the computing means and to the double integral with respect to time of the first output of the computing means, provides a signal indicative of V I r-- "r COMPUTER POSlT COHERENT ARCRAFT IAL I2 VkLOClTY DAIE'IEAI i DOPPLER mocessoa l l RADAR RADAR TARGET SYSTEM row DATA l J PATENTEUHEB YIQYI 3 6 5 4 SHEET 1 [)F 2 IO INERTIAL PLATFORM I3 AIRCRAFT INERTIAL I la I VELOCITY DATA I I DOPPLER PROCESSOR COMPUTER 1 Aw I RADAR TARGET) I POSITION DATA it??? -J FIG.I

[c MATRIX] [CK-LMATRIX] gr;

AZfd (SAMPLE 8 HOLD) s S M ,n' FILTER md DOPPLER PROCESSOR FIG. 2

INVIENT'OR.

JACOB E VALSTAR ATTORNEY PATENTEUnEc 7197! 3525414 SHEET 2 [IF 2 I I- [c MATRIX] CMMATRIXJ l 5 g V VA VM+SEANVZRAD -'SEANVZRAD A2fd (SAMPLE) QXAJQAQLEQL E) (SAMPLE a HOLD) (SAMPLE a P v FILTER l7 VMMSMOOTHED AND fd (SMOOTH-ED AND FIG. 3 commuous) commuous) [c MATRIX] [C MATRlX] [3a (CLAMP WHEN A SOLUTION fd AN RAD fig v (SAMPLE) A\ U 5E (SAMPLE) m zRAD I l -I- I5 a s FILTER \l? FILTER l8 musmoomeo AND v CONTINUOUS 'g8g *,E,%

FIG. 4

INVIL'N'I'OR.

JACOB E. VALSTAR BY l (K A/y/yw "/A/ ATTORNEY DOPPLER PROCESSING APPARATUS AND METHOD CROSS-REFERENCES TO RELATED APPLICATIONS I. U.S. application Ser. No. 670,363 filed Sept. 25, 1967 by Charles L. Vehrs, Jr., for Digital doppler Processor.

2. U.S. application Ser. No. 747,781 filed Aug. 25, 1968 by Jerome M. Page for Prediction Computation for Weapon Control.

BACKGROUND OF THE INVENTION The application of doppler processing techniques to a coherent radar system is known in the art, the description of a digital doppler processor therefor being more fully described in copending U.S. application Ser. No. 670,363 filed Sept. 25, I967 by C. L. Vehrs, Jr., assignor to North American Rockwell Corporation, assignee of the subject invention. Such reference describes the application of such a doppler processor to air-to-air modes, in which a range-gated clutterreferenced video receiver signal is doppler processed by digital means to distinguish a moving target of interest from a clutter background, the velocity of the radar platform being resolved along the antenna boresight axis, corresponding to the reference clutter velocity V or clutter centroid doppler frequency fd. Other doppler frequencies are predicted or calculated by means of integration upon a rate of change factor, AFd.

The application of a radar to a high-performance targettracking system for fire control purposes, in which vector smoothing or filtering of the target is provided in conjunction with iterative digital computing means and an inertial guidance platform is described in copending U.S. application Ser. No. 747,781 filed Aug. 25, I968, by Jerome M. Page, assignor to North American Rockwell Corporation, assignee of the subject application.

In the cooperation of such radar, iterative digital computing means and inertial guidance platform in a modern avionics weapon system, the utilization of the data of one subsystem by another subsystem of such avionics system usually involves the transformation of such data from the coordinate system of a sensing subsystem to the coordinate system of the utilizing subsystem. For example, the own ships motion data of the inertial guidance system must be transformed into that of the radar system in order to be utilized by the radar system, and the radar system data may require to be transformed from the coordinates of the radar antenna, to those of the radar system relative to the aircraft, and thence to the stabilized coordinate system of the inertial platform.

In the past, the data conversion between the coordinates of the radar system and the body axes of the utilizing aircraft has been effected by means of analog computing means comprising cosine and sine function potentiometers mounted on the gimbals of the gimballed radar system. However, such analog computing means have a limited operational life due to the mechanical wear and tear involved in the use thereof, and represent additional equipment cost and complexity. Accordingly, the avoidance of such equipment is to be preferred but heretofore has not been achieved.

SUMMARY By means of the concept of the subject invention, coordinate transformation of data in an air-to-air mode radar doppler processor is effected by increased utilization of the onboard avionics computer, whereby the use of function potentiometers mounted on the radar gimbal system is avoided.

In a preferred embodiment of the invention there is provided a doppler processor for airborne use in tracking airborne moving targets and including an inertial guidance platform, and a coherent radar having an azimuthally scanning antenna, the scan rate of which is substantially constant over all portions of the scan region. There is also included computing means for computing the on-boresight doppler velocity V, and the time rate of change VAN of the doppler velocity and comprising direction matrix conversion computing means responsive to the radar and to the inertial platform for providing a first and second output corresponding to a respective one of a preselected derivative of the doppler velocity and the product sE V where:

sE sine of ihe antenna elevation angle V platform velocity resolved in the coordinates of the A first analog integrator responsive to said first output of the radar system computing means provides a signal indicative of va and signal combining means having a first and second input,

mechanization of reduced equipment complexity and improved reliability.

These and further objects will become apparent from the following description, taken together with the accompanying drawings, in which:

DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of a system in which the concept ,of the invention may be advantageously employed;

FIG. 2 is a block diagram of one aspect of the inventive concept; and

IRAD

iRAD

kRA D FIGS. 3 and 4 are block diagrams of alternative embodiments of the invention.

In the FIGS. like reference characters refer to like parts.

DESCRIPTION OF THE PREFERRED EMBODIMENTS In an attack radar with doppler processing, the aircraft velocity component in the direction of the radar beam (V and its first derivative (v are required. The velocity component in the direction of the radar beam, determined from the azimuth (IIIAN) and elevation (E of the radar antenna, can be computed from the airframe inertial or rigid body velocities by proper Euler angle transformations. The several coordinate systems involved are:

l. The platform (inertial) coordinates, in which the platform X-axis points north (except for a small wander angle a), the Y-axis is horizontal, and the Z-axis is vertically upward.

. Airframe body coordinates in which the X-axis points forward according to the fuselage reference line (FRL), the

Yaxis is perpendicular to both the X-axis and the plane of symmetry with the positive axis on the right, and the Z- axis is in the plane of symmetry and is perpendicular to both the X- and Y-axes with the positive sense downward.

The radar X-, Y-, and Z axes, obtained by rotation from the body coordinates through the radar roll and pitch axes.

4. The radar i, j and k coordinates, obtained by rotation from the radar x, y, z coordinates through radar azimuth (da and tilt or elevation (E angles, the radar -axis corresponding to the antenna boresight axis. The complete velocity transformation from inertial coordinates (V,,, V,,,, V,,) to radar i, j, k coordinates (V V V may be represented in matrix form (with sine and cosine functions abbreviated respectively as s andc): [CEAN 0 WAN WAN AN WAN 0 0 AN 0 AN wiier'erhz dual r Such matrix representation may be represented by three component matrices, employing the radar X-, Y-, Z-axis velocity components (V V V and the body axis velocity components (V V, V a shorthand rotation being employed for each angle function matrix:

iRAD xRAD amp [EAN] ['hmlyRAD kRAD zRAD VXRAD xb VYRAD [PRAD]'[RRAD]' yb zRAD zb The prior art analytical geometry of the classical principles of such Euler angle transformations from inertial coordinates to aircraft body axis coordinates, and from aircraft body axis coordinates to radar antenna coordinates are more fully set forth in Sections 14.10-4, et seq. (pp. 473-483) of the text, Mathematical Handbook for Scientists and Engineers, by Korn and Korn (Second Edition), published by McGraw-Hill (1961 In prior art fire control radar systems employing doppler processing, the transformation from platform (inertial) coordinates to radar x, y, z coordinates (e.g., solution of equations (4) and (5)) is performed in an on-board digital computer, while the transform from radar x, y, z coordinates to radar i, j, k coordinates is performed in the radar circuitry.

The complete transformation from platform (inertial coordinates to radar x, y, z coordinates (corresponding to solution ofequations (4) and (5)) may be represented generally as:

V! xI [$1555] ikii] 6) The C matrix, as defined in equation (5a) above, is currently employed in prior art on-board computer mechanizations, while the [P l-[R l form can be stored as a single matrix:

Solving equation (8) for V FF uun C 1 .4w rnao As ims ulr.40 A- zRAl) VA the partial derivative of V with respect to w is of interest during azimuth scanning and may be obtained by differentiation with respect to 111,,

V KAIII=('-CEAN WAN nun +CEAN $4M uRAD) ll-m The rates of change of 111 are normally too high to solve equations (9) and (10) in state of the art digital computers at a sufficient iteration rate to assure sufficient accuracy. Hence, these equations have been heretofore solved in radar-connected analog devices which include sine-cosine function potentiometers attached to the antenna and related circuitry.

Although neither of equations (9) and (10) can be processed in the digital computer at a rate sufficient to provide adequate doppler compensation, it is possible to perform an alternate computation which is both adequate for such purposes and compatible with the computation rate of the computer. Such technique takes advantage of a constant azimuthal scanning rate, wherein I 41 is fixed. First, equation (9) is rearranged for convenience:

m A/v uun) I AM 'U AN VURAD) WAN AN amp) (1 1) Then (recalling that W is a constant), the derivative (V of V with respect to all may be represented as:

Ard x.v umu PM! AN+( 4N uRAD I'm I'm The parameter V as a continuous function of time, may then be determined by analog integration as the sum of l l a sampled one of a digitally computed value (V (sampled at time, t,,) and (2) the analog integral with respect to time of during the interval between successive intermittent digital computations of fd)t in this way several sine-cosine resolvers and associated analog circuitry may be eliminated from the radar system mechanization. By performing the bracketed computations of equations l l and 12) in the computer, the sine-cosine resolvers of the elevation (tilt) axis of the radar system may be eliminated; while the solution of equation (10) in the computer and extrapolation of V (by real time analog integration of V permits elimination of one sine-cosine resolver on the azimuth axis. Elimination of both sine-cosine resolvers on the azimuth axis (together with the sine-cosine resolvers on elevation axis) may be accomplished by several alternative computation arrangements, utilizing a fixed azimuthal antenna scan rate and shown generally in FIG. 1.

RAD SPRADSRRAD RAD RAD [PRAD]'[RRAD] RAD SRRAD ki] SPRAD RAD RAD RAD RAD .sflbsmming equation (7) in equation (6): "ii''rer'iifig'ifioifiiire is illustrated in block diagram V V form, a system in which the concept of the invention may be d ld ndcm 't'l V t a vantageous y emp oye a o prising an mer la 2223] [Ch] [C'k] (6a guidance platform 10 and a coherent radar system 11 having a ln the further transformation of the resolved own-ship velocity 6 from radar x, y, z coordinates to radar i, j, k coordinates (corresponding to the solution of equations (3) above), the velocity component of interest is V the own ship velocity component, resolved along the antenna boresight and corresponding to V iRAD AN 'MN AN R AN 3EAN RAD iRAD AN WAN 0 yHAD V AN PAN AN r AN AN VZRAD kRAD gdoppler processor 12 in cooperation with a digital computer 13, radar system 11 having a constant azimuthal scan rate. In such an arrangement, the second derivative (V of V may be conveniently employed, being easily computed as the dif- Ifellreritiation of [Q with respect to time, for a constant value of A 2J'II=(CEAN 14M uun CEAN 041v uRAD) W V may be computed at low cost (in terms of computer memory and computation time) by employing essentially the same parameters employed in computing V Thus, intermittent values of V V may be presented by the computer, with continuous values of V m and V, being obtained from respective integrations of the intermittent values of V m and V respectively. A term like the term sE V (in equation 9)) varies slowly, and thus can be treated as a constant between computer iterations. Accordingly, in one exemplary mechanization, the variables V and V, may be generated from V m with two analog integrators as shown in FIG. 2.

Referring to FIG. 2, there is provided direction matrix conversion means 13a and analog computing means, corresponding to computer 13 of FIG. 1 and cooperating with doppler processor 12. Matrix computing means 13a is responsive to the inertial platform 10 and radar 11 of FIG. 1 for providing a first output corresponding to the solution of equation 14) and a signal output corresponding to the term (sE V A first analog integrator 14 responsive to the sampled-and-hold first output of computing means 13a provides a signal indicative of If; while signal combining means having a first and second input responsive to a respective one of the second output of computing means 130 and the double integral (with respect to time) of the first output of computing means 13a, for computing V Such double integral is provided by a second analog integrator 16 responsively coupled to an output of first integrator 14. Resetting of the integrators l4 and 16 is synchronized with the digital computer solution (sample and hold) rate by means well understood in the art, as is indicated more fully for example in Chapter 7 of the text Electronic Analog Computers" by Korn and Korn, second edition, published by McGraw-I-Iill Book Company 1956).

The output of integrator 16, corresponding to the double integral of equation (14), is seen to also correspond to the first two products or function of ill in the right hand member of equation (10):

function (d m) PM uuo +CEAN WAN umn The combination of equation (15) and the expression, (sE V corresponding to the two inputs to summing means 15, is thus seen to correspond to equation 10) for the solution of V function (41AM) SEAN uuo =CEAN '1 zRAD +CEAN 5111A" uRAD SEAN uuo Substituting the left-hand member of equation (9) for the right-hand member of equation 16):

function ('IMN) SEAN uuu ld Thus, the exemplary mechanization of FIG. 2 is seen to provide continuously extrapolated analog signals indicative of the doppler velocity V (corresponding to the vehicle velocity resolved along the radar antenna boresight) and the rate of change of doppler velocity V The efiects of the synchronous resetting of integrators I4 and I6 and the sample-and-hold presentation of computer 130 may be preferrably smoothed by means of low-pass filters l7 and 18 (each having a cutoff frequency not exceeding the frequency of such synchronous operation).

Alternative mechanizations of such analog-interpolated sampled calculations of V,,, and V and which are less sensitive to integrator drift, are shown in FIGS. 3 and 4.

Referring to FIG. 3, there is illustrated computer 13a, integrators l4 and 16, summing means 15 and filters 17 and 18, all arranged to cooperate substantially the same as the like referenced elements of FIG. 2. Computer 130, however, also provides two additional outputs to those utilized in the arrangement of FIG. 2: a clamped third output indicative of sampled solutions for M, and a clamped fourth output indicative of sampled values for the function (V,,, +15 V The intermittent sampled and clamped solutions for V from computer 13a correct for any drift in the performance of integrator 14 as to correct the input or initial conditions of integrator 16, while the perturbation effect of such intermittent computation (and of the synchronous resetting of integrator 14) is smoothed by filter 17, prior to utilization by the doppler processor (of FIG. 1). Similarly, the intermittent sampled and clamped solution for the function, V +.rE V is combined with the sampIed-and-held function, sE V by summing means 15 to provide an intermittent computed value for V as to correct the effects of drift in integrator 16. The perturbation effect of such intermittent correction of V and of the synchronous resetting of integrator 16, is smoothed by filter 18.

An alternate mechanization for reducing the effect of integrator drift and employing only three computation outputs is shown in FIG. 4.

Referring to FIG. 4 there is illustrated computing means 13a, first and second integrators I4 and 16, summing means 15, and first and second smoothing filters l7 and 18. Computer 13a generates the sampled and held function (sE V and the sampled and clamped functions V and (V +sE V provided in the arrangement of FIG. 3. The intermittent clamped solution for V is filtered by filter 17, while the intermittent solution of V,,, formed by combining the clamped solution for (V,,, +sE V and the sampled-andheld solution for (-sE V by summing means 15, is smoothed by filter 18.

The arrangement of FIG. 4 is somewhat similar to that of FIG. 3, except that the input to integrator 14 is provided by the output of integrator 16, scaled by the scaling factor 5 Extrapolated continuous values for V V and V m may be provided continuously by means of a closed loop arrangement of synchronously-reset integrators I4 and 16, by making use of the fact that such functions are inter-related as sine and cosine functions of ill and the further fact that the amplitude of is constant. In other words, for a sinusoidal function:

f0) in lmv i il f/ w C05 LAN l df/d =1 N in um 20) the relative amplitude of the derivative varies as the frequency or time rate of change of the argument, while the second derivative varies as the square of the frequency.

Referring to equations (9), l0) and 14), for the respective determinations of V,,,, V and V it is seen that the bracketed term in equation I) is the partial derivative of equation (9), and that the related amplitude of the periodic function of equation (10) to that of equation (9) is in the ratio ILAN and that the bracketed term in equation (14) is the partial second derivative of equation l0), and that the amplitude ratio of such second derivative, V to the partial function for ia is 9 ml Referring again to FIG. 4, the output of integrator 16 is seen to represent the integral of V and also the double integral of the input of integrator 14, which double integral, when scaled by the scaling factor (III corresponds to the derivative function, V Thus, by so scaling the output of integrator 16 by scaling means 19 (such as an adjustable-gain, phase-inverting amplifier or the like), a signal corresponding to the partial second derivative (V of V is generated. Such partial second derivative may then be continuously in terpolated by successive ones of serially interconnected integrators 14 and 16 to provide interpolated values for V M and the partial function for V during the unclamped (nonsampling) intervals during which computer 13a is not providing the solutions VA m and m ain)- Accordingly, the closed loop integrator arrangement of FIG. 4 utilizes fewer computer solutions to effect compensation for integrator drift, while also providing continuous interpolations for V and V between the intervals of the computer solutions.

Thus, it is to be appreciated that means have been described for increased utilization of an onboard computer in a doppler processor, whereby analog sine and cosine function generators may be eliminated from the radar system, thus efiecting economies in system equipment without sacrificing system functional integrity and accuracy.

Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of k illustration and example only and is not to be taken by way of limitation; the spirit and scope of this invention being limited only be the terms of the appended claims.

I claim:

- 1, In a .doppler processor. system including an inertial guidance platform and'a coherent radar having an azimuthally scanning antenna, the scan rate of which is substantially constant over all portions of the scan region, means for computing the on-boresight doppler velocity V and the time rateofchange of the doppler velocity V M and comprising direction matrix conversion computing means responsive to said radar and to said inertial platform for providing a first and second output corresponding to a respective one of a preselected derivative of the doppler velocity and the product SEAN V where: sE sine of the antenna elevation angle in the coordinates of the radar system; V m platform velocityresolved in the. coordinates of the radar system; i I l l a first analog integrator responsive to said first output of said computing means-for providing .a signal indicative of V and g signal combining means having a first and second input responsive toa respective one. of said second output of said computing means and to a preselected integral with respect to time of said first output of said computing means for providing a signal indicative of V 2. The device of claim 1 in whichsaid signal combining:

means includes said first analog integrator.

3. The device of claim 1 in which said signal combining means includes a second analog integrator responsively cou-: pled to an output of said first analog integrator for generating said preselected integral of-saidv first output of said integrating means.

4. The device of claim 1 in which said signal combining means comprises a second analog integrator responsively. coupled to anoutput of said first integrator;

analog means responsive to art-output of said second integrator and to said second output of said computing means for providing an output indicative of the analog sum thereof; and a first low-pass filter responsive to an output of said summing means and having a cutofifrequency not ex-- ceeding a sampling rate of said computing means.

5. The device claim 1 in which said computing means further provides a third and fourth periodically sampled output corresponding to a respective one of V4, and the sum (V +35 V, ,,-')'of V and said product sE V said third output of said computing means being coupled with said output of said first analog integrator, and said fourth output of said computing means being coupled to said second input of said signal combining means.

6. The device of claim 1 in which said computing means further'provides a third and fourth periodically sampled output corresponding to a respective one of Vi m and the sum V, +sE V of V and said product :8 V said third output of said computing means being coupled with said output of said first analog integrator, and said fourth output of said comfurther provides a periodically sampled third output corresponding to the sum (V +sE V of the 'doppler Y velocity V and said product SEAN V said third output being coupled with the output of said first analog integrator.

and in turn there is further provided a second analog integrator responsive to said coupled to third output of said computing means and having an output coupled with said first output of said computing mcans; and a first and second low-pass filter respectively coupled to a respective output of said signal combining'm-eans and said second integrator, each said filter having cutoff frequency 

1. In a doppler processor system including an inertial guidance platform and a coherent radar having an azimuthally scanning antenna, the scan rate of which is substantially constant over all portions of the scan region, means for computing the onboresight doppler velocity Vfd and the time rate of change of the doppler velocity V fd and comprising direction matrix conversion computing means responsive to said radar and to said inertial platform for providing a first and second output corresponding to a respective one of a preselected derivative of the doppler velocity and the product sEANVzRAD, where: sEAN sine of the antenna elevation angle in the coordinates of the radar system; VzRAD platform velocity resolved in the coordinates of the radar system; a first analog integrator responsive to said first output of said computing means for providing a signal indicative of V fd; and signal combining means having a first and second input responsive to a respective one of said second output of said computing means and to a preselected integral with respect to time of said first output of said computing means for providing a signal indicative of Vfd.
 2. The device of claim 1 in which said signal combining means includes said first analog integrator.
 3. The device of claim 1 in which said signal combining means includes a second analog integrator responsively coupled to an output of said first analog integrator for generating said preselected integral of said first output of said integrating means.
 4. The device of claim 1 in which said signal combining means comprises a second analog integrator responsively coupled to an output of said first integrator; analog means responsive to an output of said second integrator and to said second output of said cOmputing means for providing an output indicative of the analog sum thereof; and a first low-pass filter responsive to an output of said summing means and having a cutoff frequency not exceeding a sampling rate of said computing means.
 5. The device of claim 1 in which said computing means further provides a third and fourth periodically sampled output corresponding to a respective one of V fd and the sum (Vfd+sEANVzRAD) of Vfd and said product sEANVzRAD, said third output of said computing means being coupled with said output of said first analog integrator, and said fourth output of said computing means being coupled to said second input of said signal combining means.
 6. The device of claim 1 in which said computing means further provides a third and fourth periodically sampled output corresponding to a respective one of V fd and the sum (Vfd+sEANVzRAD) of Vfd and said product sEANVzRAD, said third output of said computing means being coupled with said output of said first analog integrator, and said fourth output of said computing means being coupled to said second input of said signal combining means, and in which there is provided a first and second low-pass filter respectively responsive to a respective output of said signal combining means and said first analog integrator, each said filter having a cutoff frequency not exceeding a sampling rate of said computing means.
 7. The device of claim 1 in which said computing means further provides a periodically sampled third output corresponding to the sum (Vfd+sEANVzRAD) of the doppler velocity Vfd and said product sEANVzRAD, said third output being coupled with the output of said first analog integrator, and in which there is further provided a second analog integrator responsive to said coupled third output of said computing means and having an output coupled with said first output of said computing means; and a first and second low-pass filter respectively coupled to a respective output of said signal combining means and said second integrator, each said filter having a cutoff frequency not in excess of the sampling rate of said computing means. 